Single Photon Finding Study

The effectiveness of the V1 peak finder and a square peak finder for sparse photon events are compared below. The square peak finder finds pixels above a specific threshold which are contained within a 2x2 area allowing for 1, 2, 3 or 4 pixel photons then the rest of the remaining square is included which contributes the most to the photon energy. This makes the assumption that photon create square peaks on detectors.

The data from experiment xcs06016 and run 37 were used in this analysis. Only sparse events were used so multiple photon peaks or pixels shared by multiple photons are extremely rare; events with less than 3000 peaks found by each peak finder were used. A total of 13 events were used. The purpose of these analyses is to determine which (if any) of the following methods discussed below have an appreciable effect on the RMS of the distribution of the energy.

Comparing Peak Finders

V1 vs. Square

The distribution of events for each peak finder is shown below. In the plot next to it, the square peak finder distribution is manually shifted by -4.8 to compare the shapes of the distribution which appear to be very similar.

One can see that the peaks roughly follow a Gaussian distribution but on the higher end, there is a very noticeable shoulder. At first, it appears to be a result of dense photons, a situation that was avoided. With the use of sparse events. A Gaussian curve was fitted to both distributions but to ignore the effects of the shoulder, only the data within 15 ADU of the bin with the maximum number of peaks was used so as to center the data used in the fit around the peak of the Gaussian. The result from this was the V1 peak finder having a mean of 141.93 ± 0.06 and a standard deviation of 8.37 and the square peak finder having a mean of 146.68 ± 0.060 and a standard deviation of 8.20 where the errors were obtained by σ/√N.

Just to confirm the suspicions, the sparsest event, event 634, was looked at separately. The V1 and square peak finders found only 545 and 584 peaks, respectively. It can be seen in the energy distribution of the peaks for event 634 that the high energy shoulder is still present so it cannot be due to multiple photon complications. Furthermore, by manually checking peaks, it can be seen that the high energy peaks do not neighbor other peaks and are merely just higher energy peaks.

One possible explanation is how the peaks are chosen. For the square peak finder, since the 2x2 region with the highest energy is chosen to complete the square for 1 and 2 pixel photons, it is possible that this includes noise that is higher than average thus shifting the total energy above the mean. Likewise for the V1 peak finder, large noise has a greater chance of being included since it may surpass the lower threshold again shifting the total energy of the peak above the mean.

It is possible that this shoulder is partly due to the K-beta emission of the material used in this particular experiment which happens to be copper (while the main peak is the K-alpha emission). After a quick loop-up, these values for copper are approximately 8040 keV for K-alpha and 8900 keV for K-beta which gives a 1.107 ratio of K-beta to K-alpha. If we look at the distribution of just the maximum energy pixel of each peak, as shown below, there is very visibly some type of peak on the higher energy side of the 1 pixel distribution. The main peak has a mean of 140.3 while the mean of the smaller peak is about 155. This gives a ratio of 1.104. The numbers used are approximations and the second peak is artificially shifted by the Gaussian from the first peak underlying it. So it is very likely that these two peaks are the K-alpha and K-beta lines of copper.

Closer Look at the Effect of Pixel Size

Since the square peak finder only find 4 pixel peaks, only the data for the V1 peak finder is shown below.  This data consists of 29,342 peaks found from the 13 different events.

Pixels	Peaks	Mean	Error	RMS
1	7164	140.24	0.09	7.45
2	14926	142.54	0.07	8.24
3	4354	141.53	0.17	11.44
4	2898	146.58	0.18	9.70

Lining up and Recombining Pixel Distributions

As can be seen in the table above, there is a noticeable difference in the means of the energy distributions for each number of pixels which, ideally, shouldn't exist. Furthermore, the errors on the mean cannot account for this difference. One theory is that the larger peaks (the ones with more pixels) end up adding in more noise to the total energy of the photon thus shifting it to a slightly higher energy. If such is the case, one remedy would be to shift each distribution so that their peaks fall on the same bin. This was done by using the average of the four bins where the peaks existed as the new bin for the peaks. Below is the result compared to the normal distribution shown in the first graph on this page. As can be seen, the difference is very slight; the distribution is slightly sharper for the shifted data, but not by very much.

When fit with a Gaussian in the same manner as before, the results confirm this observation. Although there is a decrease in the width, it is very small. The noticeable change in the mean is most likely due to the choice of energy used to which the peaks were shifted.